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Given a field F and an extension field K superset= F, an element alpha in K is called algebraic over F if it is a root of some nonzero polynomial with coefficients in F. ...

Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).

A function f(x) is said to have bounded variation if, over the closed interval x in [a,b], there exists an M such that |f(x_1)-f(a)|+|f(x_2)-f(x_1)|+... +|f(b)-f(x_(n-1))|<=M ...

A centered polygonal number consisting of a central dot with four dots around it, and then additional dots in the gaps between adjacent dots. The general term is n^2+(n+1)^2, ...

A check which can be used to verify correct computations in a table of grouped classes. For example, consider the following table with specified class limits and frequencies ...

Let z=x+iy and f(z)=u(x,y)+iv(x,y) on some region G containing the point z_0. If f(z) satisfies the Cauchy-Riemann equations and has continuous first partial derivatives in ...

Let P be the principal (initial investment), r be the annual compounded rate, i^((n)) the "nominal rate," n be the number of times interest is compounded per year (i.e., the ...

Given a triangle, draw a Cevian to one of the bases that divides it into two triangles having congruent incircles. The positions and sizes of these two circumcircles can then ...

A surface of constant negative curvature obtained by twisting a pseudosphere and given by the parametric equations x = acosusinv (1) y = asinusinv (2) z = ...